Related papers: Learning Chaos In A Linear Way

Learning high-performance deep neural networks for dynamic modeling of high Degree-Of-Freedom (DOF) robots remains challenging due to the sampling complexity. Typical unknown system disturbance caused by unmodeled dynamics (such as internal…

In this paper, we introduce a modular deep neural network (DNN) framework for data-driven reduced order modeling of dynamical systems relevant to fluid flows. We propose various deep neural network architectures which numerically predict…

Physical systems whose dynamics are governed by partial differential equations (PDEs) find applications in numerous fields, from engineering design to weather forecasting. The process of obtaining the solution from such PDEs may be…

Data-driven models for predicting dynamic responses of linear and nonlinear systems are of great importance due to their wide application from probabilistic analysis to inverse problems such as system identification and damage diagnosis. In…

Port-Hamiltonian neural networks (pHNNs) are emerging as a powerful modeling tool that integrates physical laws with deep learning techniques. While most research has focused on modeling the entire dynamics of interconnected systems, the…

Singularly perturbed dynamical systems play a crucial role in climate dynamics and plasma physics. A powerful and well-known tool to address these systems is the Fenichel normal form, which significantly simplifies fast dynamics near slow…

A physics-informed convolutional neural network is proposed to simulate two phase flow in porous media with time-varying well controls. While most of PICNNs in existing literatures worked on parameter-to-state mapping, our proposed network…

We present a numerical method to learn an accurate predictive model for an unknown stochastic dynamical system from its trajectory data. The method seeks to approximate the unknown flow map of the underlying system. It employs the idea of…

Fault detection in rotating machinery is a complex task, particularly in small and heterogeneous dataset scenarios. Variability in sensor placement, machinery configurations, and structural differences further increase the complexity of the…

Reservoir computing systems, a class of recurrent neural networks, have recently been exploited for model-free, data-based prediction of the state evolution of a variety of chaotic dynamical systems. The prediction horizon demonstrated has…

Traffic problems have seriously affected people's life quality and urban development, and forecasting the short-term traffic congestion is of great importance to both individuals and governments. However, understanding and modeling the…

This paper explores Neural Operators to predict turbulent flows, focusing on the Fourier Neural Operator (FNO) model. It aims to develop reduced-order/surrogate models for turbulent flow simulations using Machine Learning. Different model…

In chaotic dynamical systems such as the weather, prediction errors grow faster in some situations than in others. Real-time knowledge about the error growth could enable strategies to adjust the modelling and forecasting infrastructure…

Predicting the evolution of complex systems governed by partial differential equations (PDEs) remains challenging, especially for nonlinear, chaotic behaviors. This study introduces Koopman-inspired Fourier Neural Operators (kFNO) and…

Recently, physics-driven deep learning methods have shown particular promise for the prediction of physical fields, especially to reduce the dependency on large amounts of pre-computed training data. In this work, we target the…

Predicting the dynamics of chaotic systems is one of the most challenging tasks for neural networks, and machine learning in general. Here we aim to predict the spatiotemporal chaotic dynamics of a high-dimensional non-linear system. In our…

Chaos arises in many complex dynamical systems, from weather to power grids, but is difficult to accurately model using data-driven emulators, including neural operator architectures. For chaotic systems, the inherent sensitivity to initial…

Many research works deal with chaotic neural networks for various fields of application. Unfortunately, up to now these networks are usually claimed to be chaotic without any mathematical proof. The purpose of this paper is to establish,…

The control of complex systems is of critical importance in many branches of science, engineering, and industry. Controlling an unsteady fluid flow is particularly important, as flow control is a key enabler for technologies in energy…

Identifying latent interactions within complex systems is key to unlocking deeper insights into their operational dynamics, including how their elements affect each other and contribute to the overall system behavior. For instance, in…